1. If x² - y² = 55, and x - y = 11, then y = 2. If the slope of a line is ½ and the y- intercept is 3, what is the x-intercept of the same line?

Transcription

1 1/20/2016 SAT Warm-Up 1. If x² - y² = 55, and x - y = 11, then y = 2. If the slope of a line is ½ and the y- intercept is 3, what is the x-intercept of the same line?

2 Simple Interest = Pin where P = principal (original amount borrowed/loaned) i = interest rate for one period n = number of periods Ex: You borrow $10,000 for 3 years at 5% simple annual interest. interest = P x i x n = 10,000 x.05 x 3 = 1,500 Ex: You borrow $10,000 for 60 days at 5% simple interest per year (assume a 365 day year). interest = P x i x n = 10,000x.05x(60/365) =

3 The effective rate is the actual rate that you earn on an investment or pay on a loan after the effects of compounding frequency are considered. Effective Rate = (1 + (i/n)) n 1 Where: i = Nominal or stated interest rate n = Number of compounding periods per year Ex: What effective rate will a stated annual rate of 6% yield when compounded semiannually? Effective Rate = ( / 2) 2 1 = Continuous Compound Interest A = Pe rt where, P = principal amount (initial investment) r = annual interest rate (as a decimal) t = number of years A = amount after time t

4 An amount of $2, is deposited in a bank paying an annual interest rate of 3.1%, compounded continuously. Find the balance after 3 years. An amount of $1, is deposited in a bank paying an annual interest rate of 2.85 %, compounded continuously. Find the balance after 2½ years. An amount of $2, is deposited in a bank paying an annual interest rate of 2.85 %, compounded continuously. (a) Find the balance after 3 years. (b) How long would it take for the money to double? (a)

5 (b) 2000 e t = 4000 e t = 4000/2000 = 2 Now solve the exponential equation, e t = 2, by converting it into log notation. This will give us, t = log e t = ln2 t = ln2 / t =

6 A# Compound Interest and e Worksheet The history of mathematics is marked by the discovery of special numbers such as or i. Another special number is denoted by the letter e. It is called the Euler number after its discoverer and it is also called the natural base e. Like, it is an irrational number. n 1 lim 1 e n n It is important to remember that e is JUST A NUMBER! One use of e is for continuously compounded interest. where P = principal investment A t rt Pe r = interest rate (as a decimal) t = time There is another formula we can use to calculate interest when it is not compounded continuously: For compounding interest a specific # of times annually: where P = principal investment r A( t) P 1 n nt r = interest rate (as a decimal) t = time n = # of times you compound annually 1) If you invest $2500 in an account, what is the balance in the account and the amount of interest after 4 years if you earn: a) 1.7% interest compounded annually? b) 1.5% compounded monthly? c) 1.2% compounded daily? d) 0.7% compounded continuously?

7 2) Martha makes an investment of $500 in an account that pays 6% interest compounded monthly. a) Write an equation you could use to determine the interest she earns in t years. b) How much money will Martha have in her account one year from now if she never withdraws any money and reinvests the interest? c) What is the effective annual rate for this account (think about what percent of her money has she earned at the end of one year)? 3) A credit card company charges 12.9% annual interest. a) If they compound interest monthly, how much will you owe for every dollar you do not pay off for a year? b) If they compound interest daily, how much will you owe for every dollar you do not pay off for a year? c) What is the effective annual rate in the situation above? 4) An initial investment of $700 is worth $725 a year later. What is the effective annual yield for this account? 5) A loan shark lends a gambler $1, to cover a debt. He charges 35% annual interest compounded continuously. How much does the gambler owe the loan shark at the end of one year? Two years? 6) The value of a $25,000 car depreciates at a rate of 12% per year. What will the car be worth in 5 years?

8 -1- W H2W0f1s2C YKGu9ttaG gsgomf2tbwlasrhe0 VL9LCCE.F f damlslk 4ruiUgJhdtAs7 Erxesszetr 8v9eGdE.b 5 4MtapdJeo TwFi9twhK EIcnRfyiwnLigtKe9 LPnrGef-WAKlrg8e2bsr Baa.P Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name Simple and Compound Interest Use simple interest to find the ending balance. 1) $34,100 at 4% for 3 years 2) $210 at 8% for 7 years Date Period 3) $4,000 at 3% for 4 years 4) $20,600 at 8% for 2 years 5) $14,000 at 6% for 9 years 6) $2,300 at 7% for 9 years 7) $43,800 at 4.8% for 2 years 8) $35,800 at 8.2% for 3 years 9) $7,400 at 10.5% for 1 4 years 10) $1,900 at 5.9% for years

9 -2- M w2s0q1b2f OKXu4tZaa rs8odfytuwqa2rter 0LYLpCa.z K IAklMle MrCiVg5hhtcsz Nrte1syeLr1v0e4dH.t 2 ympazdxeh qw0istbhd hizn0fgixnpijtae0 bphrfec- yatlkgieqburxal.t Worksheet by Kuta Software LLC Find the total value of the investment after the time given. 11) $7,300 at 7% compounded semiannually for 3 years 12) $1,030 at 4% compounded 13) $18,000 at 9% compounded semiannually for 6 years 14) $1,500 at 7% compounded annually for 3 years 15) $1,240 at 8% compounded annually for 2 years 16) $55,000 at 16% compounded 17) $28,600 at 7.9% compounded 18) $21,000 at 13.6% compounded quarterly for 4 years 19) $12,700 at 8.8% compounded semiannually for 1 year 20) $130 at 9.4% compounded quarterly for 2 years

10 -1- v H2f0U1R2A xkruotjaz YSRo7f7tVwaaNrhed 8LtLKCx.u 2 cawl3ld 2raiOgahit9sr 6r3essgexr 7vLeydO.P 9 omwaidbew tw2ijtzhc DIgntf2ibneietAea sp4rkel-8a0l1gpelbirvad.m Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name Simple and Compound Interest Use simple interest to find the ending balance. Date Period 1) $34,100 at 4% for 3 years $38, ) $210 at 8% for 7 years $ ) $4,000 at 3% for 4 years $4, ) $20,600 at 8% for 2 years $23, ) $14,000 at 6% for 9 years $21, ) $2,300 at 7% for 9 years $3, ) $43,800 at 4.8% for 2 years $48, ) $35,800 at 8.2% for 3 years $44, ) $7,400 at 10.5% for 1 4 years $7, ) $1,900 at 5.9% for years $2,208.28

11 -2- H 42b041f2n GK7uytiaB PSno2f3t4wbaJrDeY OLcLnCp.5 s RAdlXl0 Wr6ibg8hptgsC trye0s0errsv7ekdu.c l lmiandweh kwfiot8hx MIUnPfLiQn6i5t2es fpmrgek-paolxgtebbsrua8.s Worksheet by Kuta Software LLC Find the total value of the investment after the time given. 11) $7,300 at 7% compounded semiannually for 3 years $8, ) $1,030 at 4% compounded $1, ) $18,000 at 9% compounded semiannually for 6 years $30, ) $1,500 at 7% compounded annually for 3 years $1, ) $1,240 at 8% compounded annually for 2 years $1, ) $55,000 at 16% compounded $74, ) $28,600 at 7.9% compounded $33, ) $21,000 at 13.6% compounded quarterly for 4 years $35, ) $12,700 at 8.8% compounded semiannually for 1 year $13, ) $130 at 9.4% compounded quarterly for 2 years $ Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com